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2 years ago

Solve for x. 2x² +21x-61 = (x+7)² Please

Mathematics

2 answers:

Ymorist [56]2 years ago

7 0

Answer:

$x = \frac{-7 +\sqrt{489} }{2}$

$x = \frac{-7 - \sqrt{489} }{2}$

Step-by-step explanation:

2x² +21x-61 = (x+7)²

expand

2x² + 21x - 61 = x² + 14x +49

move everything to one side

x² + 7x - 12 = 0

use quadratic formula

$x = \frac{-b +- \sqrt{b^{2}-4ac } }{2a}$

plug in the values

$x = \frac{-7 +- \sqrt{7^{2}-4(1)(-110) } }{2(1)}$

solve

$x = \frac{-7 +- \sqrt{49-4(1)(-110) } }{2}$

$x = \frac{-7 +- \sqrt{49 + 440 } }{2}$

$x = \frac{-7 +- \sqrt{489} }{2}$

noname [10]2 years ago

5 0

After you rewrite the equation, identify the coefficients , substitute the coefficients and simplify the expression you’ll be left with 489

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Two lighthouses are located 75 miles from one another on a north-south line. If a boat is spotted S 40o E from the northern ligh

yuradex [85]

Answer:

The northern lighthouse is approximately $24.4\; \rm mi$ closer to the boat than the southern lighthouse.

Step-by-step explanation:

Refer to the diagram attached. Denote the northern lighthouse as $\rm N$ , the southern lighthouse as $\rm S$ , and the boat as $\rm B$ . These three points would form a triangle.

It is given that two of the angles of this triangle measure $40^{\circ}$ (northern lighthouse, $\angle {\rm N}$ ) and $21^{\circ}$ (southern lighthouse $\angle {\rm S}$ ), respectively. The three angles of any triangle add up to $180^{\circ}$ . Therefore, the third angle of this triangle would measure $180^{\circ} - (40^{\circ} + 21^{\circ}) = 119^{\circ}$ (boat $\angle {\rm B}$ .)

It is also given that the length between the two lighthouses (length of $\rm NS$ ) is $75\; \rm mi$ .

By the law of sine, the length of a side in a given triangle would be proportional to the angle opposite to that side. For example, in the triangle in this question, $\angle {\rm B}$ is opposite to side $\rm NS$ , whereas $\angle {\rm S}$ is opposite to side ${\rm NB}$ . Therefore:

$\begin{aligned} \frac{\text{length of NS}}{\sin(\angle {\rm B})} = \frac{\text{length of NB}}{\sin(\angle {\rm S})} \end{aligned}$ .

Substitute in the known measurements:

$\begin{aligned} \frac{75\; \rm mi}{\sin(119^{\circ})} = \frac{\text{length of NB}}{\sin(21^{\circ})} \end{aligned}$ .

Rearrange and solve for the length of $\rm NB$ :

$\begin{aligned} & \text{length of NB} \\ =\; & (75\; \rm mi) \times \frac{\sin(21^{\circ})}{\sin(119^{\circ})} \\ \approx\; & 30.73\; \rm mi\end{aligned}$ .

(Round to at least one more decimal places than the values in the choices.)

Likewise, with $\angle {\rm N}$ is opposite to side ${\rm SB}$ , the following would also hold:

$\begin{aligned} \frac{\text{length of NS}}{\sin(\angle {\rm B})} = \frac{\text{length of SB}}{\sin(\angle {\rm N})} \end{aligned}$ .

$\begin{aligned} \frac{75\; \rm mi}{\sin(119^{\circ})} = \frac{\text{length of SB}}{\sin(40^{\circ})} \end{aligned}$ .

$\begin{aligned} & \text{length of SB} \\ =\; & (75\; \rm mi) \times \frac{\sin(40^{\circ})}{\sin(119^{\circ})} \\ \approx\; & 55.12\; \rm mi\end{aligned}$ .

In other words, the distance between the northern lighthouse and the boat is approximately $30.73\; \rm mi$ , whereas the distance between the southern lighthouse and the boat is approximately $55.12\; \rm mi$ . Hence the conclusion.

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2 years ago

Which would be an equivalent way to write y= 2 - 3x ?

Fudgin [204]

The answer is B, because the numbers in the equation are 2, and -3x. The signs have to stay with the numbers they are with. So if you move the 3 to the front you have to keep the negative with it.

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2 years ago

What percent of 25$ is 5$ no links

liraira [26]

Answer:

20%

Step-by-step explanation:

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2 years ago

Read 2 more answers

Determine the unknown angles in the diagram above. Please help!

Nana76 [90]

a and 143 are supplementary. So a + 143 = 180

a + 143 = 180 Subtract 143 from both sides.

a = 180 - 143

a = 37

b and 143 are vertically opposite angles and are equal

b = 143 degrees.

Interior angles on the same side of a transversal for parallel lines are supplementary

b + c = 180

143 + c = 180

c = 37

c + d + 85 = 180 degrees

37 + d + 85 = 180

d + 122 = 180

d = 180 - 122

d = 58

e = c They are vertically opposite.

e =37

All triangles have 180 degrees.

e + f + 90 = 180 degrees.

37 + f + 90 = 180

f + 127 = 180

f = 180 - 127

f = 53

G and 48 are opposite 2 equal sides. So G and 48 are equal

G = 48

h + 48 + 48 = 180

h + 96 = 180

h = 84

K and H are supplementary

K + H = 180

k + 84 = 180

k = 95

m+ k + d = 180

M + 95 + 58 = 180

M + 143 = 180

M = 37

the top angle is 2*m and 2m is bisected. You are using the m on the left.

P + 85 + M = 180

P + 85 + 37 = 180

P + 122 = 180

p = 180 - 122

p = 58

r + p are supplementary.

r + p = 180

r + 58 = 180

r = 180 - 58

r = 122

s + r + c + b = 360 All quadrilaterals have 360 degrees.

s + 122 + 37 + 143 = 360

s + 302= 360

s = 360 - 302

s = 58

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jekas [21]

Step-by-step explanation:

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